The minimum speed that a simple pendulum's bob should be given so that it rises to a level where its string makes \(60^\circ\) with the vertical is:
A block of \(1\) kg is released from the top of a smooth curve \(\mathrm{AB},\) and then it encounters a rough surface \(\mathrm{BC},\) coming to rest at \(\mathrm{C}.\) The work done by friction is:
(take \(g=10\) m/s2)
1. | \(25\) J | 2. | \(50\) J |
3. | \(-25\) J | 4. | \(-50\) J |
The work done by all the forces (external and internal) on a system equals the change in:
1. | total energy | 2. | kinetic energy |
3. | potential energy | 4. | none of these |
1. | \(\dfrac{\pi}{6}\) | 2. | \(\dfrac{\pi}{3}\) |
3. | \(\dfrac{\pi}{2}\) | 4. | \(\dfrac{2\pi}{3}\) |
1. | zero | 2. | \(-\frac12mu^2cos^2\theta\) |
3. | \(-\frac12mu^2sin^2\theta\) | 4. | \(-\frac12mu^2\) |